A Space-Saving Approximation Algorithm for Grammar-Based Compression

Sakamoto, Hiroshi; Maruyama, Shirou; Kida, Takuro; Shimozono, Shinichi

doi:10.1587/transinf.e92.d.158

Cited by 27 publications

(18 citation statements)

References 21 publications

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“…These results confirm that IRR-MC finds the smallest grammars as was suggested in [9]. Until now, no other polynomial time algorithm (including theoretical algorithms that were designed to achieve a low approximation ratio [1,2,21]) has proven (theoretically nor empirically) to perform better than IRR-MC.…”

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confidence: 74%

The Smallest Grammar Problem as Constituents Choice and Minimal Grammar Parsing

et al. 2011

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Abstract:The smallest grammar problem-namely, finding a smallest context-free grammar that generates exactly one sequence-is of practical and theoretical importance in fields such as Kolmogorov complexity, data compression and pattern discovery. We propose a new perspective on this problem by splitting it into two tasks: (1) choosing which words will be the constituents of the grammar and (2) searching for the smallest grammar given this set of constituents. We show how to solve the second task in polynomial time parsing longer constituent with smaller ones. We propose new algorithms based on classical practical algorithms that use this optimization to find small grammars. Our algorithms consistently find smaller grammars on a classical benchmark reducing the size in 10% in some cases. Moreover, our formulation allows us to define interesting bounds on the number of small grammars and to empirically compare different grammars of small size.

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confidence: 74%

The Smallest Grammar Problem as Constituents Choice and Minimal Grammar Parsing

et al. 2011

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“…An algorithm computes D 1 , D 2 for w 1 , w 2 respectively. We assume that all variables are appropri- [13] within a good approximation ratio, which is, however, not implemented. We thus modify this compression algorithm to fit our problem of detecting long common substrings, and we show a lower bound to guarantee the length of the extracted pattern.…”

Section: Introductionmentioning

confidence: 99%

Scalable Detection of Frequent Substrings by Grammar-Based Compression

Nakahara

Maruyama

Kuboyama

et al. 2013

IEICE Trans. Inf. & Syst.

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SUMMARYA scalable pattern discovery by compression is proposed. A string is representable by a context-free grammar deriving the string deterministically. In this framework of grammar-based compression, the aim of the algorithm is to output as small a grammar as possible. Beyond that, the optimization problem is approximately solvable. In such approximation algorithms, the compressor based on edit-sensitive parsing (ESP) is especially suitable for detecting maximal common substrings as well as long frequent substrings. Based on ESP, we design a linear time algorithm to find all frequent patterns in a string approximately and prove several lower bounds to guarantee the length of extracted patterns. We also examine the performance of our algorithm by experiments in biological sequences and other compressible real world texts. Compared to other practical algorithms, our algorithm is faster and more scalable with large and repetitive strings.

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“…Sakamoto et al [25] proposed the LCA algorithm that requires O(g * log g * ) space with linear running time and O(log n log g * )-approximation ratio. LCA was modified to achieve O(log n log * n)-approximation ratio within O(n log * n) running time [26], where log * n, called the iterated logarithmic function, is the number of times the log function is applied to n to produce a constant. On the other hand, Gagie and Gawrychowski [27] proposed O(min(g * , n log n))-approximation algorithm in a streaming model where the algorithm works in constant space and logarithmic passes over a constant number of streams.…”

Section: Introductionmentioning

confidence: 99%

An Online Algorithm for Lightweight Grammar-Based Compression

2012

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Grammar-based compression is a well-studied technique to construct a context-free grammar (CFG) deriving a given text uniquely. In this work, we propose an online algorithm for grammar-based compression. Our algorithm guarantees O(log 2 n)-approximation ratio for the minimum grammar size, where n is an input size, and it runs in input linear time and output linear space. In addition, we propose a practical encoding, which transforms a restricted CFG into a more compact representation. Experimental results by comparison with standard compressors demonstrate that our algorithm is especially effective for highly repetitive text.

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A Space-Saving Approximation Algorithm for Grammar-Based Compression

Cited by 27 publications

References 21 publications

The Smallest Grammar Problem as Constituents Choice and Minimal Grammar Parsing

The Smallest Grammar Problem as Constituents Choice and Minimal Grammar Parsing

Scalable Detection of Frequent Substrings by Grammar-Based Compression

An Online Algorithm for Lightweight Grammar-Based Compression

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